Horizontal Lines
Answer the following questions given the line graphed below.
- Explain why the line graphed above represents a linear relationship.
- Create a table containing all the defined ordered pairs shown in the graph.
- What do you notice about all the \(y\)-values in the table?
- What is the slope of this line? What method did you use to calculate the slope?
- What is the \(y\)-intercept of this line? Name this point as an ordered pair.
- What equation could be used to represent any point on this line?
- Is this equation in the slope-intercept form?
Horizontal lines have slopes that are in the form \(\dfrac{rise}{run}=\dfrac{0}{a}=0\), where \(a\) is an element of the complex numbers.
All horizontal lines have a slope of zero and thus, equations (written in slope-intercept form) are in the form \(y=0x+b\), which is the same as \(y=b\).
In the graph shown above, \(b=3\) and all points have the \(y\)-value of \(3\) for any value of \(x\). In this example, the equation for this horizontal line is \(y=3\).